The goal of this research study is to learn more about the effectiveness or benefit, of recombinant human growth hormone (a hormone that promotes muscle growth) in the treatment of wasting associated with AIDS. Prior studies comparing recombinant human growth hormone with placebo (an inactive Look-alike substance) have shown that growth hormone is useful in increasing in lean body mass (muscle) and physical function. In this study, the benefits of growth hormone will be measured by comparing the amount of exercise performed before and after treatment. An additional aim of this study is to determine the optimal, or best, dose of growth hormone for the treatment of the HIV-associated wasting based on change in lean body mass. Loss of lean vody mass is associated with an increased risk of death in persons with AIDS.